Is second hand smoke dangerous for a person recovering from a pulmonary embolism?

Yes. Second-hand smoke is dangerous for anyone, regardless of whether they're recovering from an acute illness or not. However, if you are recovering from an embolism, it would be best to avoid anything like second-hand smoke that might cause difficulty breathing or coughing.
Not directly. Second hand smoke does not directly influence the recovery from pe but in principle is bad for anybody with a breathing problem.